A camshaft phaser of the generic type is disclosed, for example, in European patent specification EP 1 979 582 B1. In its basic structure, the camshaft phaser has a stator that can be driven by a crankshaft and a rotor that is non-rotatably joined to the camshaft. Between the stator and the rotor, there is an annular space that is divided into several working chambers by means of projections which protrude radially inwards and which are non-rotatably joined to the stator, each of said chambers being divided into two pressure spaces by means of a vane that protrudes radially outwards from the rotor. Depending on the charging of the pressure chambers with a pressure medium, the rotor is phased either in the “early” or “late” direction with respect to the stator, and thus also the camshaft with respect to the crankshaft. The pressure build-up of the pressure medium likewise takes place via the crankshaft, as a result of which only a slight flow of pressure medium is provided at low rotational speeds. This slight stream of pressure medium has the disadvantage that, under unfavorable conditions, an undesired change in the setting of the camshaft phaser can occur which, in turn, can lead to unfavorable operating behavior on the part of the internal combustion engine, especially during the cold-start phase, along with unfavorable consumption values and rough running. For this reason, the camshaft phaser disclosed in European patent specification EP 1 979 582 B1 proposes a helical torsion spring between the rotor and the stator. A radially outer end of the torsion spring is attached to a projection associated with the stator, while a radially inner end of the torsion spring is attached to a pin associated with the rotor. The helical spring is secured towards the outside by means of a cover that is pressed into a ring-cylindrical projection of the stator.